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COMPLETELY DISTINGUISHABLE PROJECTIONS OF SPATIAL GRAPHS

RYO NIKKUNI

Department of Mathematics, Faculty of Education, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan

https://doi.org/10.1142/S0218216506004282Cited by:2 (Source: Crossref)

Abstract

A generic immersion of a finite graph into the 2-space with p double points is said to be completely distinguishable if any two of the 2^p embeddings of the graph into the 3-space obtained from the immersion by giving over/under information to each double point are not ambient isotopic in the 3-space. We show that only non-trivializable graphs and non-planar graphs have a non-trivial completely distinguishable immersion. We give examples of non-trivial completely distinguishable immersions of several non-trivializable graphs, the complete graph on n vertices and the complete bipartite graph on m + n vertices.

Keywords:

AMSC: 57M25, 05C10

References

Y. Huh and K. Taniyama, J. Knot Theory Ramifications 13, 991 (2004). Link, Web of Science, Google Scholar
W. K. Mason, Trans. Amer. Math. Soc. 142, 269 (1969). Web of Science, Google Scholar
R. Nikkuni, J. Knot Theory Ramifications 9, 387 (2000). Link, Web of Science, Google Scholar
N. Hartsfield and G. Ringel , Pearls in Graph Theory , A comprehensive Introduction ( Academic Press, Inc. , Boston, MA , 1994 ) . Google Scholar
I. Sugiura and S. Suzuki, Sci. Math. 3, 193 (2000). Google Scholar
N. Tamura, J. Knot Theory Ramifications 13, 211 (2004). Link, Web of Science, Google Scholar
K. Taniyama, Topology 33, 509 (1994). Crossref, Web of Science, Google Scholar
K. Taniyama, Proc. Amer. Math. Soc. 123, 3575 (1995). Crossref, Web of Science, Google Scholar
K. Taniyama, Topol. Appl. 65, 205 (1995). Crossref, Web of Science, Google Scholar
W. T. Wu, Sci. Sinica 9, 21 (1960). Google Scholar